German website

study programs: Bachelor of Computer Science (B_Inf), Computer Engineering (B_Tinf), Media Computer Science (B_Minf), Business and Computer Science (B_Winf), 1st semester

ECTS credits: 4

lecture term: summer and winter semester

prerequesites: precalculus mathematics of secondary school

language: This lecture is always given in German (sorry!)

This lecture gives the mathematical fundamentals for further study in all computer science programs. The contents are highly related to a lot of parallel and subsequent courses.

Besides standard material such as logics and proof concepts, set theory, number theory, combinatorics, and graph theory, we also give an introduction in group and field theory which highlights in the construction algorithm for arbitrary finite fields. For exercises, some construction programs implemented by students of FH Wedel in a software project may be downloaded here  (instructions in German).

This lecture is complemented by exercises lead by teaching assistants.

The material covered is summarized in German slides published on the German website of this lecture. You also find some other links to German literature there. I am planning to publish a book from my lecture notes in cooperation with my colleague Prof. Lang. This book may appear in 2010 (in German).

 1. Fundamentals of mathematics
    1.1 Motivation
    1.2 Propositional logic
    1.3 Predicate logic

2. Set theory
    2.1 Fundamentals
    2.2 Relations
    2.3 Functions
    2.4 Boolean algebras

3. Proof concepts
    3.1 Glossary of mathematical structures
    3.2 Complete induction
    3.3 Other proof strategies

4. Number theory
    4.1 Divisibility
    4.2 Dividing with remainders
    4.3 Prime numbers
    4.4 Modular arithmetic

6. Combinatorics
    6.1 Enumaration formulas for sets
    6.2 Permutations

7. Graph theory
    7.1 Terminology und representation
    7.2 Path problems in graphs (including Dijkstra's algorithm)
    7.3 Trees (including Kruskal's algorithm)
    7.4 Planar graphs
    7.5 Colouring graphs

All literature cited is written in German except for the book of Biggs. The book of Dean also originates from an English original, but this book is only on an introductory level below the main level of this lecture and only covers the material of the first 3 weeks.

text books

Albrecht Beutelspacher / Marc-Alexander Zschiegner: Diskrete Mathematik für Einsteiger, Vieweg 2004 (2. Auflage), ISBN 3-528-16989-3

Sebastian Iwanowski / Rainer Lang: Neues Vorlesungsskript für die Vorlesung Diskrete Mathematik, FH Wedel 2010 (internal document only accessible for students of FH Wedel)

Christoph Meinel / Martin Mundhenk: Mathematische Grundlagen der Informatik, Teubner 2002 (2. Auflage), ISBN 3-519-12949-3

further books for topics covered in this lecture:

Martin Aigner: Diskrete Mathematik, Vieweg 2001 (4. ed.), ISBN 3-528-37268-0

Norman L. Biggs: Discrete Mathematics, Oxford University Press 2002, ISBN 0-19-850717-8

Neville Dean: Diskrete Mathematik, Pearson Studium, Reihe "im Klartext" 2003, ISBN  3-8273-7069-8

Dirk Hachenberger: Mathematik für Informatiker, Pearson Studium 2005, ISBN 3-8273-7109-0

Hans Kurzweil: Endliche Körper, Springer 2007, ISBN 978-3-540-49081-4

Jiri Matousek / Jaroslav Nesetril: Diskrete Mathematik - Eine Entdeckungsreise, Springer-Verlag 2001, ISBN 3-540-42386-9

Gerald Teschl / Susanne Teschl: Mathematik für Informatiker, Band 1: Diskrete Mathematik und Lineare Algebra, Springer 2008 (3. Auflage), ISBN 978-3-540-77431-0

literature for broadening the mathematical horizon:

Martin Aigner: Graphentheorie - Eine Entwicklung aus dem 4-Farben-Problem, Teubner 1984, ISBN 3-519-02068-8

Martin Aigner / Ehrhard Behrends: Alles Mathematik - Von Pythagoras zum CD-Player, Vieweg 2002 (2. Auflage), ISBN 3-528-13131-4

Martin Aigner / Günter Ziegler: Proofs from THE BOOK, Springer-Verlag 2010 (4. ed.), ISBN 978-3-642-00855-9